The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  3  1  1  1  1  1  1  1  1  1  1  1  1  1  1  3  1  1  1  1  1  3  1  0  1  1  1  3
 0  3  0  0 24 21 15  3 24 21 18  0 21 15  9 24 24 21 15 21 18 15 18  3 15  9 21 12 24  6 18  3  9  6  3 15  9 18 21 15 24 12  0 21 24  0  0 18  3 21 12 21 15  0 15  9 18  3 24  6 18  3  6  0 24 24  3  9  0  3  9  3 21  0
 0  0  3 24  0 15 21  3  6  6 21  0  3 21 15  9  6  0 18  6  3 21 18 18  6 24 21 12 15  0  9 24  3 12 21  6  6 18 18 18 12  0 18 24  0 24 24 18  3  0 24 18 21  3  3 18 21  3 21  9  6 21 15  3 12 15 24 15 24  6 15 15 18 24
 0  0  0  9  0  0 18  0  0  9 18  9 18  9 18  0  9 18 18  9  0  0 18  9 18  0 18 18 18  9 18  9  9 18  0  9 18  9 18  0  0  9  0  0  9 18  0  9  9  0 18  9  9 18 18  0  0  0 18 18  0  0  0  9  9  9  0 18 18 18  0 18  9  0
 0  0  0  0  9 18  0  9 18  0 18  9  0  0  0  0  9 18 18  9  9  9 18  9 18  9 18  9  0  0  0 18  0 18 18 18 18 18  0 18 18 18 18  0 18  9  9  0  9  9  0  0  9  0  9  9 18  0  9  9 18 18  0  9 18 18  9 18 18  9 18  9 18  0

generates a code of length 74 over Z27 who´s minimum homogenous weight is 138.

Homogenous weight enumerator: w(x)=1x^0+554x^138+1022x^141+108x^142+1434x^144+648x^145+1944x^146+1572x^147+4212x^148+3888x^149+1380x^150+864x^151+850x^153+540x^156+330x^159+224x^162+88x^165+22x^168+2x^207

The gray image is a code over GF(3) with n=666, k=9 and d=414.
This code was found by Heurico 1.16 in 3.52 seconds.